New York city. It’s about ten times bigger than Indianapolis, and about a bazillion times more famous. But to physicists Luis Bettencourt and Geoffrey West, NYC is just Indianapolis with seven million extra people. That’s because hidden beneath the apparent diversity of different cities, they’ve found certain patterns showing up again and again. These bizarrely uniform patterns suggest that, given enough people, Indianapolis would have the cultural and economic clout of NYC. But they also suggest that we have been making a fundamental mistake every time we try to understand what makes a city healthier, wealthier, or better looking than its rivals.
The patterns Bettencourt, West and their colleagues uncovered relate to population size. If you told them the population of any city in the US, without knowing anything else about it, they could give you a pretty accurate prediction of its vital statistics: average income, infrastructure, crime rate, disease prevalence. That’s because most of these figures change regularly with population size in one of two ways:
The bigger the city, the more efficient (by 15%)
The more people that live in a city, the more infrastructure is needed, like gas stations, electrical cables and roads. Thanks to economies of scale, that infrastructure also gets more efficient. This is not an unfamiliar idea; in a bigger city, people are closer together, they travel shorter distances, more municipal resources are shared. But what Bettencourt and West showed is that this increase in efficiency always has the same magnitude. A city with twice as many people as another has more infrastructure than the smaller city, but has about 15% less infrastructure per person. That figure is about the same, whether you’re looking at roads or pipelines, and whether you are looking at the difference between a city of 100,000 people vs. 200,000 people, or the difference between a city of 1 million people vs. 2 million people.
The bigger the city, the more productive (by 15%)
Some factors are the outcomes of interactions between people. These include both good outcomes – like innovation and wealth – and bad outcomes– like crime and disease. Because social interactions increase with population size, so do these outcomes. But as for infrastructure efficiency, these social factors not only increase with size but also become increasingly productive with size. That means both per person wealth and crime rates increase, but again with the same regular pattern: a doubling of the population results in an increase in a 15% increase in productivity per person.
West thinks these patterns are telling us something fundamental about the ways cities work – he is looking for a ‘unified theory of cities’ (ahh, physicists). I think we need to see more work from this group to decide how important these ‘laws’ are, but there is one thing they have convinced me of. We need to take these patterns into account when we compare cities. Traditionally, we look at measurements expressed per capita (divide the measurement by the number of people in the city). But while NYC has more crime per capita than Indianapolis, that is mostly a consequence of its size. What we really want to know is whether NYC has more crime per capita than predicted by its size. That is how we could tell whether some local factor – town planning, law enforcement, politics, history, geography – is playing an important role in crime rates.
Bettencourt and West have made a start on these kinds of comparisons. They looked at the stats for every city in the US corrected for population size. Some cities, like NYC and Indianapolis, are just about average for their size. Other cities are unusual for their size, suggesting the influence of local factors. Some aspects of a city seem to be more susceptible to the influence of local quirks than others. For example, the population size of any city predicts its gross metropolitan product (income) with about 93% confidence. However, you can only predict the annual number of patents arising from the same city with about 67% confidence. That means that in many cases, things other than population size are driving rates of technical innovation.
Like in Corvallis, Oregon. This city of 80,000 peopled filed 128% more patents than predicted from its size alone, making it the most disproportionately innovative city in the US. Corvallis, Oregon? That would be the home of Oregon State University and a large Hewlett-Packard operation that in its glory days developed the commercial inkjet printer. As an aside, it is also the least religious county in the nation, the one with the most Peace Corps volunteers, and the one with the most green buildings. You get the picture. Meanwhile, the average personal income in this creative city is only about 10% greater than predicted by its size. The question that now arises is whether the cause of Corvallis’ uniqueness is simply the Hewlett-Packard campus, or whether some other unique factors are at play. Corvallis would certainly hope it’s the latter, given the layoffs that have drastically reduced Hewlett-Packard’s local operations.
I first heard about this work during a talk by West at his academic home, the Santa Fe Institute, which brings together experts in modelling complex systems. The talk was being given at the fabulous Santa Fe Science Writing Workshop, and West’s audience consisted of of science writers and scientists hungry for a story for their writing assignment. After the talk, I was buzzing with excitement but surprised that the reception from the others was lukewarm. Everyone agreed the work was fascinating, West had given brilliant presentation, and they were now overflowing with stories. But they also agreed that the whole project was clearly mad. The chemist was skeptical of how squeaky clean the correlations were. The historian saw all the crucial details of history whitewashed out.
When I read accounts of this work in the press, critics mostly complained that West isn’t telling us anything we don’t know. Others pointed out that this work doesn’t tell us anything about what makes one city different from another.
But aside from suspicion of the actual data processing (which I can’t critique), I think these criticisms miss the point. Looking at common trends isn’t a way to deny the effects of history and politics – it’s a way to highlight them. If you don’t believe me, you should spend some time playing with the interactive maps they generated from the US data. Get used to the interface by tracking the performance of your favourite city over time, then start to notice the profound influence of history in the patterns of red and blue dots. West’s approach just quantifies the things we might guess –the US is unequal, crime and patents and money are linked to human capital– and tells us where to start looking for informative exceptions.
Bettencourt LMA, Lobo J, Strumsky D, West GB (2010) Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities. PLoS ONE 5(11): e13541.
Bettencourt LMA, Lobo J,Helbing, D, Kühnert C, West GB (2007) Growth, innovation, scaling, and the pace of life in cities. PNAS e13541. 104(17):7301-7306